The present invention relates to semiconductor integrated circuits. More specifically, the invention relates to a technique that can be effectively adapted to structure of an active filter, such as structure of a switched-capacitor filter in a semiconductor integrated circuit which contains a filter circuit.
Filters used for transmission lines have developed from LC filters employing individual parts to RC active filters employing operational amplifiers. In recent years, switched-capacitor filters are used in which a resistance element in the active filter has been replaced by a switch and a capacitor.
When an active filter having desired frequency characteristics is to be designed, in general, a transfer function is first found which satisfies the desired filter characteristics, the transfer function is decomposed into a primary or a secondary rational expression, a basic block is designed which realizes the characteristics for the rational expression, and the basic blocks are connected in cascade.
In designing the switched-capacitor filter, a Z-function is used to express the transfer function instead of using a Laplace-transformed S-function. The relation between the Z-function and the S-function is represented by Z=e.sup.ST (e=natural logarithm, T; sampling period). If S is replaced by J.omega. (.omega.: angular velocity) to express in terms of a complex number, the relation is represented by Z=e.sup.j.omega.t.
As primary switched capacitor filters that realize characteristics given by a transfer function H(Z)=(C+DZ.sup.-1)/(A+BZ.sup.-1) represented by the Z-function, circuits have already been proposed as shown in FIGS. 1 and 2 (IEEE, Solid-state circuits, Vol. SC-14, No. 6, Dec., 1979, pp. 1020-1033, MOS Switched-Capacitor Analog Sampled Data Direct Form Recursive Filters, Ian. A. Young; ISCAS, 1980, General Active Switched-Capacitor Biquad Topology For Precision MOS Filters, K. R. Laker, pp. 304-308).
In the circuit form shown in FIG. 1, however, if the individual capacitors are denoted by C.sub.0, C.sub.1, C.sub.2 and C.sub.5, a charge transfer equation at a moment (nT) at which the individual switches are under the condition shown in FIG. 1, is given by, ##EQU1##
If the charge transfer equation is subjected to the Z-conversion to find the transfer function H(Z), the following equation (2) is obtained, i.e., ##EQU2##
It will therefore be understood that the coefficients A to D in the general equation H(Z)=(C+DZ.sup.-1)/(A+BZ.sup.-1) of the transfer function of the primary filter are given as A=C.sub.5 +C.sub.0, B=-C.sub.0, C=C.sub.1 +C.sub.2, D=-C.sub.1.
In the circuit form of FIG. 1, therefore, when it is desired to realize a filter which has characteristics with a very low so-called zero point (frequency at which the numerator of the transfer function becomes zero), it is necessary to bring C/D, i.e., to bring (C.sub.1 +C.sub.2)/C.sub.1 to approximately "1". Here, to bring (C.sub.1 +C.sub.2)/C.sub.1 close to "1" means that the capacitance C.sub.2 must be reduced to be very much smaller than the capacitance C.sub.1. In semi-conductor integrated circuits, however, a limitation is imposed on reducing the area of capacitors as determined by a minimum processable dimension in the manufacturing process. To bring (C.sub.1 +C.sub.2)/C.sub.1 to "1", therefore, the capacitance C.sub.1 must be increased to be very much larger than the capacitance C.sub.2.
In the circuit employing a filter of the form shown in FIG. 1, therefore, the capacitor C.sub.1 occupies an increased area, and the chip size increases. Further, load capacitance increases for the operational amplifier that forms input the signal V.sub.1 in the preceding stage, which is not shown. Therefore, the operational amplifier OP.sub.1 operates at a decreased speed, and consumes an increased amount of electric power.
If the ratio of capacitor C.sub.1 to capacitor C.sub.2 is decreased to decrease the area, frequency characteristics of the filter deteriorate, and accuracy decreases.
In the case of the circuit of FIG. 2, switches S.sub.31, S.sub.32 coupled to the capacitor C.sub.3 operate at a timing deviated by a half period relative to switches S.sub.41, S.sub.42 coupled to the capacitor C.sub.4, as shown in FIG. 3. Therefore, data of a half period ago is stored in the capacitor C.sub.4.
In the circuit form of FIG. 2, therefore, the following charge transfer equation (3) holds true: ##EQU3##
If the equation (3) is subjected to the Z-conversion to find a transfer function H(Z), the following equation (4) is obtained: EQU H(Z)=(C.sub.3 -C.sub.4 .multidot.Z.sup.-1/2)/{(C.sub.0 +C.sub.5)-C.sub.0 Z.sup.-1 } (4)
where Z.sup.-1 and Z.sup.-1/2 denote operators that mathematically represent data (quantities of analog signals) of one period ago and a half period ago.
In the equation (3), if it is presumed that V.sub.1 {(n-1/2)T}=V.sub.1 {(n-1)T}, an equation (5) of the form of primary/primary is obtained, i.e., EQU H(Z)=-(C.sub.3 -C.sub.4 .multidot.Z.sup.-1)/{(C.sub.0 +C.sub.5)-C.sub.0 .multidot.Z.sup.-1 } (5)
If it is attempted to realize a filter having the circuit form shown in FIG. 2 with characteristics having a low zero point as described above, C.sub.3 /C.sub.4 must be brought close to "1" as will be understood from the equation (5). This can be accomplished relatively easily; i.e., C.sub.3 =C.sub.4 should be realized. Unlike the circuit form of FIG. 1, the ratio of capacitances does not become large, and the chip size does not increase, either.
Here, the above-mentioned presumption V.sub.1 {(n-1/2)T}=V.sub.1 {(n-1)T} has a meaning that the data of one period ago must be equal to the data of a half period ago. With the circuit form of FIG. 2, however, the above requirement does not hold true. To satisfy the above presumption, therefore, it is necessary to provide a sample holding circuit in a stage preceding the circuit of FIG. 2 to hold the data of one period ago up to the moment of a half period ago.
However, the sample holding circuit is constituted by using, for example, a switched-capacitor and an operational amplifier. This means that the substrate constituting a semiconductor integrated circuit requires additional area for the sample holding circuit, resulting in the increase in power consumption, too. For instance, when a tertiary filter is to be constituted by using the circuit of FIG. 2, the area occupied by the sample holding circuit and the power consumption thereof become as large as about one-fourth the whole values.